Why do conservatives think they can get away with making false claims?

Because they can. Conservatives have the MSM terrified of the 'liberal media' label, which they pin aggressively to anyone who actually calls them on their constant lies.The media lets the lies p through, and dozens of conservative talkers all repeat the exact same point unchallenged, with the goal of making it appear to be a fact. That's why most of the country thinks the stimulus bill was a failure, even though it's impossible to find an actual economist who thinks so. It's why a large minority believes to this day that Saddam Hussein helped organize 9/11.